A Grey Hat in the computer security community, refers to a skilled hacker who sometimes acts legally, sometimes in good will, and sometimes not. They are a hybrid between white and black hat hackers. They usually do not hack for personal gain or have malicious intentions, but may or may not occasionally commit crimes during the course of their technological exploits.
One reason a grey hat might consider himself to be grey is to disambiguate from the other two extremes: black and white. It might be a little misleading to say that grey hat hackers do not hack for personal gain. While they do not necessarily hack for malicious purposes, grey hats do hack for a reason, a reason which more often than not remains undisclosed. A grey hat will not necessarily notify the system admin of a penetrated system of their penetration. Such a hacker will prefer anonymity at almost all cost, carrying out their penetration undetected and then exiting said system still undetected with minimal damages. Consequently, grey hat penetrations of systems tend to be for far more passive activities such as testing, monitoring, or less destructive forms of data transfer and retrieval.
A person who breaks into a computer system and simply puts their name there whilst doing no damage (such as in wargaming - see) can also be classified as a grey hat.